A conventional connection between a one-way clutch or brake element and another transmission element in a gear transmission includes conventional splines in which a plurality of parallel spline teeth is formed integrally with a race of the clutch or brake element and a plurality of spline tooth spaces is formed in a mating transmission element. Such spline connections are capable of transmitting heavy torques but they have inherent drawbacks, such as the relatively high manufacturing cost and the need for aligning the mating spline teeth for assembly. Furthermore, the backlash between the mating spline teeth that prevents the teeth from jamming together causes shock loading upon clutch or brake engagement and speed change, such as during shifting. This may cause damaging shock loading and/or vibration upstream and/or downstream in the torque flow path.
One publication entitled "A Better Way To Make Shaft Connections" by David Ryffel, found in MACHINE DESIGN magazine dated Aug. 11, 1988 at page 124, discusses the use of a polygonal profile in a torque transmitting connection for locking a shaft to a hub. The connection comprises polygonal lobes on a shaft which register with polygonal internal spaces on a hub.
Another publication entitled "Locating Nodes On Radially Loaded Rings" by David Hustvedt and found in MACHINE DESIGN magazine dated Apr. 10, 1986 discusses use of a differential bending equation to calculate node point locations on a circular ring subjected to equal, uniformly spaced radial loads.